The line limiting the space occupied by a flat geometrical figure is called perimeter. In a polygon this broken line includes all parties therefore for calculation of length of perimeter it is necessary to know length of each of the parties. In regular polygons of length of pieces between tops are identical that allows to simplify calculations.

## Instruction

1. For calculation of length of perimeter of the wrong polygon you should find out available means length of each of the parties separately. If this figure is represented on the drawing, determine the sizes of the parties, for example, by means of a ruler and put the received sizes - result and will be required **perimeter**.

2. The polygon can be set in statements of the problem by coordinates of the tops. In this case consistently calculate length of each of the parties. Use coordinates of points (for example A (X ₁, Y ₁), B (X ₂, Y ₂)) limiting pieces which are the parties of a figure. Find the difference of coordinates of these two points along each of axes (X -X ₂ and Y -Y ₂), square the received sizes and put. Then take a root from the received value: √ ((X -X ₂)² + (Y -Y ₂)²) is and there will be length of the party between tops of A and B. Do this operation for each pair of next tops then put the calculated lengths of the parties to learn perimeter length.

3. If in statements of the problem it is told that the polygon is regular and also the number of its tops or the parties is given, for finding of perimeter there is enough calculation of length of only one party. If coordinates are known, calculate it in the way described above, and increase the received value in the number of times equal to the number of the parties to calculate perimeter.

4. At the number of the parties (n) of a regular polygon, known from statements of the problem, and diameter (D) of the circle described about it, length of perimeter (P) can be calculated with use of trigonometrical function - a sine. Determine length of the party by multiplication of the known diameter by a sine of the angle which size is equal 180 °, divided into the number of the parties: D*sin (180 ° / n). For calculation of perimeter as it was told in the previous step, increase the received value by number of the parties: P = D*sin (180 ° / n*n.

5. Too it is possible to determine perimeter by the known diameter (d) of the circle entered in a regular polygon with the set number of tops (n) (P). In this case the formula of calculation will differ from described in the previous step only by the trigonometrical function used in it - replace a sine with a tangent: P = d*tg (180 ° / n*n.